Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Multiply the following using the vertical multiplication method:

[tex]\[
\begin{array}{l}
3x^2 - 5x + 1 \\
\times (x^2 + 2x + 4) \\
\hline
\end{array}
\][/tex]

A. [tex]\(3x^4 - x^3 + 3x^2 + 18x + 4\)[/tex]

B. [tex]\(3x^4 + x^3 + 10x^2 + x + 4\)[/tex]

C. [tex]\(3x^4 + x^3 + 3x^2 - 18x + 4\)[/tex]

D. [tex]\(3x^4 + x^3 + 10x^2 - 18x + 4\)[/tex]

Sagot :

GinnyAnswer
To multiply the given polynomials [tex]\( 3x^2 - 5x + 1 \)[/tex] and [tex]\( x^2 + 2x + 4 \)[/tex] using the vertical multiplication method, follow these steps:

### Step-by-Step Process

1. List the Polynomials:
- First Polynomial: [tex]\( 3x^2 - 5x + 1 \)[/tex]
- Second Polynomial: [tex]\( x^2 + 2x + 4 \)[/tex]

2. Multiply Each Term Independently:

- Multiply [tex]\( 3x^2 \)[/tex] by Each Term in [tex]\( x^2 + 2x + 4 \)[/tex]:
- [tex]\( 3x^2 \cdot x^2 = 3x^4 \)[/tex]
- [tex]\( 3x^2 \cdot 2x = 6x^3 \)[/tex]
- [tex]\( 3x^2 \cdot 4 = 12x^2 \)[/tex]

- Multiply [tex]\(-5x\)[/tex] by Each Term in [tex]\( x^2 + 2x + 4 \)[/tex]:
- [tex]\(-5x \cdot x^2 = -5x^3 \)[/tex]
- [tex]\(-5x \cdot 2x = -10x^2 \)[/tex]
- [tex]\(-5x \cdot 4 = -20x \)[/tex]

- Multiply [tex]\( 1 \)[/tex] by Each Term in [tex]\( x^2 + 2x + 4 \)[/tex]:
- [tex]\( 1 \cdot x^2 = x^2 \)[/tex]
- [tex]\( 1 \cdot 2x = 2x \)[/tex]
- [tex]\( 1 \cdot 4 = 4 \)[/tex]

3. Combine All the Results:
- [tex]\( 3x^4 \)[/tex]
- [tex]\( 6x^3 + (-5x^3) = x^3 \)[/tex]
- [tex]\( 12x^2 + (-10x^2) + x^2 = 3x^2 \)[/tex]
- [tex]\(-20x + 2x = -18x \)[/tex]
- [tex]\( 4 \)[/tex]

4. Sum the Combined Results:
- [tex]\( 3x^4 + x^3 + 3x^2 - 18x + 4 \)[/tex]

### Conclusion
Therefore, the final result of multiplying [tex]\( 3x^2 - 5x + 1 \)[/tex] by [tex]\( x^2 + 2x + 4 \)[/tex] using the vertical multiplication method is:

[tex]\[ 3x^4 + x^3 + 3x^2 - 18x + 4 \][/tex]

Thus, the correct answer is:

C. [tex]\( 3x^4 + x^3 + 3x^2 - 18x + 4 \)[/tex]
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.